A spokesman for Russian President Vladimir Putin said the rift with Turkey will not be resolved overnight despite Ankara's apology for the downing of a Russian military jet last year (AP)

It will take time to mend ties between Russia and Turkey following the downing of a military jet, a spokesman for Russian President Vladimir Putin has said.

Turkish president Recep Tayyip Erdogan sent a letter of formal apology to Mr Putin on Monday, seven months after Turkey shot down the Russian jet on a mission in Syria, triggering a slew of Russian sanctions that have dealt a severe blow to the Turkish economy.

Mr Putin's spokesman Dmitry Peskov called the apology "a very important" step, but added that ties between the two nations will not be repaired overnight.

"Together we will have to take more than one step to meet each other," Mr Peskov said. "One shouldn't think that everything will be mended overnight. We will keep up our work in that direction."

Mr Putin will talk to Mr Erdogan by telephone on Wednesday, which will be their first one-to-one chat since the jet was shot down in November.

Mr Putin denounced the downing of the jet as a "treacherous stab in the back". Russia rejected the Turkish claim that the plane had violated its airspace, and responded by deploying long-range air defence missiles to its base in Syria and warned it would destroy any target posing a threat to Russian aircraft.

The incident came amid a rift between Moscow and Ankara over Syria, where they backed the opposing sides in the conflict.

Moscow moved swiftly to ban the sale of package tours to Turkey, which had depended heavily on the Russian tourist flow; banned most of Turkey's food exports; and introduced restrictions against Turkish construction companies, which had won a sizeable niche of the Russian market.

In contrast to Mr Peskov, Turkish PM Binali Yildirim said on Tuesday that the ties are already getting better: "We can say that the ice has melted and that the process of normalisation has started."

Along with the formal apology, Moscow said it expects Ankara to pay compensation to the family of the killed pilot.

Asked about the possible compensation, Mr Yildirim said in comments carried by the Anadolu news agency that "there is no such thing. We only expressed our regrets, we shared their grief".

He added that Turkey will go ahead with the prosecution of the men responsible for the pilot's death.